Physics 101: Lecture 24 Ideal Gas Law and Kinetic Theory€¦ · Physics 101: Lecture 24, Pg 15...
Transcript of Physics 101: Lecture 24 Ideal Gas Law and Kinetic Theory€¦ · Physics 101: Lecture 24, Pg 15...
Physics 101: Lecture 24, Pg 1
Physics 101: Physics 101: Lecture 24Lecture 24Ideal Gas Law and Kinetic Ideal Gas Law and Kinetic
TheoryTheory Today’s lecture will cover Textbook Chapter 13.5-13.7
EXAM III
Physics 101: Lecture 24, Pg 2
Aside: The Periodic TableAside: The Periodic Table
Physics 101: Lecture 24, Pg 3
The Periodic Table The Periodic Table Explained ?Explained ?
protonneutronelectron
Look carefully
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Energy vs Mass Energy vs Mass
He (m=4.0026 u) O (M=15.9995 u)
4 x He = 16.01 u
Mass difference = 0.01 u = binding energy
So energy is the same as mass somehow ??
E = mc2 (phys 102)
Physics 101: Lecture 24, Pg 5
Molecular Picture of GasMolecular Picture of Gas Gas is made up of many individual molecules
Number density is number of molecules/volume:N/V = /m is the mass densitym is the mass for one molecule
Number of moles: n = N / NANA = Avogadro’s Number = 6.022x1023 mole-1
Mass of 1 mole of “stuff” in grams = molecular mass in u (or amu)e.g., 1 mole of N2 has mass of 2x14=28 grams
Physics 101: Lecture 24, Pg 6
Atomic Act IAtomic Act IWhich contains the most molecules ? 1. A mole of water (H2O)2. A mole of oxygen gas (O2)3. Same H2O
O2
correct
Physics 101: Lecture 24, Pg 7
Atomic Act IIAtomic Act IIWhich contains the most atoms ? 1. A mole of water (H2O)2. A mole of oxygen gas (O2)3. Same
H2O (3 atoms)
O2 (2 atoms)
correct
Physics 101: Lecture 24, Pg 8
Atomic Act IIIAtomic Act IIIWhich weighs the most ? 1. A mole of water (H2O)2. A mole of oxygen gas (O2)3. Same
H2O (M = 16 + 1 + 1)
O2 (M = 16 + 16)
correct
Physics 101: Lecture 24, Pg 9
The Ideal Gas LawThe Ideal Gas Law P V = N kB TP = pressure in N/m2 (or Pascals)V = volume in m3
N = number of moleculesT = absolute temperature in Kk B = Boltzmann’s constant = 1.38 x 10-23 J/KNote: P V has units of N-m or J (energy!)
P V = n R Tn = number of molesR = ideal gas constant = NAkB = 8.31 J/mol/K
Physics 101: Lecture 24, Pg 10
Ideal Gas Law ACT IIdeal Gas Law ACT IPV = nRTPV = nRT
You inflate the tires of your car so the pressure is 30 psi, when the air inside the tires is at 20 degrees C. After driving on the highway for a while, the air inside the tires heats up to 38 C. Which number is closest to the new air pressure?
1) 16 psi 2) 32 psi 3) 57 psi
Careful, you need to use the temperature in K
P = P0 (38+273)/(20+273)
Physics 101: Lecture 24, Pg 11
Ideal Gas Law: ACT IIIdeal Gas Law: ACT IIpV = nRTpV = nRT
A piston has volume 20 ml, and pressure of 30 psi. If the volume is decreased to 10 ml, what is the new pressure? (Assume T is constant.)
1) 60 2) 30 3) 15
V=20
P=30V=10
P=??When n and T are constant, pV is constant (Boyle’s Law)
Physics 101: Lecture 24, Pg 12
Balloon ACT 1Balloon ACT 1
What happens to the pressure of the air inside a hot-air balloon when the air is heated? (Assume V is constant)
1) Increases 2) Same 3) Decreases
Balloon is still open to atmospheric pressure, so it stays at 1 atm
Physics 101: Lecture 24, Pg 13
Balloon ACT 2Balloon ACT 2
What happens to the buoyant force on the balloon when the air is heated? (Assume V remains constant)
1) Increases 2) Same 3) Decreases
FB = V g
is density of outside air!
Physics 101: Lecture 24, Pg 14
Balloon ACT 3Balloon ACT 3
What happens to the number of air molecules inside the balloon when the air is heated? (Assume V remains constant)
1) Increases 2) Same 3) Decreases
PV = NkT
P and V are constant. If T increases N decreases.
Physics 101: Lecture 24, Pg 15
Lecture 24,Lecture 24, Preflight 2Preflight 2In terms of the ideal gas law, explain briefly how a hot air balloon works.
The flame lifts the balloon because it gets rid of the air inside, making it lighter inside.
Note! this is not a pressure effect, it is a density effect. As T increases, the density decreases the balloon then floats due to Archimedes principle. The pressure remains constant!
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Ideal Gas Law: DemosIdeal Gas Law: DemospV = nRTpV = nRT
When T is constant, pV is constant (Boyle’s Law)Boyle’s law demo
When p is constant, V is proportional to Thelium and oxygen in LN2
When V is constant, p is proportional to TExplosion!
Physics 101: Lecture 24, Pg 17
Kinetic Theory:Kinetic Theory:The relationship between energy and temperatureThe relationship between energy and temperature(for (for monatomicmonatomic ideal gas)ideal gas)
Lxx mvp 2
xvLt 2
tpF x
avg
L
mvtp xx
2
AFP
VNmvx
2
For N molecules, multiply by N
Note KE = ½ m v2 = 3/2 m vx2
trKVNP
32
Using PV = NkT
kTKtr 23
means average.
kT/2 energy per degree of freedom = equipartition theorem
Physics 101: Lecture 24, Pg 18
Preflight 1Preflight 1
63%
19%
18%
0% 20% 40% 60% 80%
Suppose you want the rms (root-mean-square) speed of molecules in a sample of gas to double. By what factor should you increase the temperature of the gas? 1. 22.3. 4
2
correctTk
23 vm
21
B2 KE
• If v doubles, v2 quadruples
• Therefore, T quadruples
root-mean-square?
Physics 101: Lecture 24, Pg 19
Example Example What is the rms speed of a nitrogen (N2)
molecule in this classroom?
Tk23 BKE
Tk23 vm
21
B2
mTk3 v B2
kg/u) 101.66(u) (2820)KJ/K)(273 1038.1(3 v 27-
232
v = 510 m/s
= 1150 mph!
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Hints for final examHints for final exam
Lectures 25-28 will be
over-represented.
There will be m
any problesm
taken from
the quizzes.
Physics 101: Lecture 24, Pg 21
SummarySummary
Ideal Gas Law PV = n R TP = pressure in N/m2 (or Pascals)V = volume in m3
n = # molesR = 8.31 J/ (K mole)T = Temperature (K)
Kinetic Theory of Monatomic Ideal Gas<Ktr> = 3/2 kB T